{"id":"https://openalex.org/W3066108421","doi":"https://doi.org/10.3390/sym12081379","title":"On Taylor Series Expansion for Statistical Moments of Functions of Correlated Random Variables","display_name":"On Taylor Series Expansion for Statistical Moments of Functions of Correlated Random Variables","publication_year":2020,"publication_date":"2020-08-18","ids":{"openalex":"https://openalex.org/W3066108421","doi":"https://doi.org/10.3390/sym12081379","mag":"3066108421"},"language":"en","primary_location":{"id":"doi:10.3390/sym12081379","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081379","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1379/pdf?version=1597930639","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/8/1379/pdf?version=1597930639","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037345422","display_name":"Luk\u0103\u0161 Nov\u00e1k","orcid":"https://orcid.org/0000-0001-9387-2745"},"institutions":[{"id":"https://openalex.org/I60587646","display_name":"Brno University of Technology","ror":"https://ror.org/03613d656","country_code":"CZ","type":"education","lineage":["https://openalex.org/I60587646"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Luk\u00e1\u0161 Nov\u00e1k","raw_affiliation_strings":["Faculty of Civil Engineering, Brno University of Technology, 60200 Brno, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0001-9387-2745","affiliations":[{"raw_affiliation_string":"Faculty of Civil Engineering, Brno University of Technology, 60200 Brno, Czech Republic","institution_ids":["https://openalex.org/I60587646"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079548498","display_name":"Drahom\u00edr Nov\u00e1k","orcid":"https://orcid.org/0000-0003-0744-8265"},"institutions":[{"id":"https://openalex.org/I60587646","display_name":"Brno University of Technology","ror":"https://ror.org/03613d656","country_code":"CZ","type":"education","lineage":["https://openalex.org/I60587646"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Drahom\u00edr Nov\u00e1k","raw_affiliation_strings":["Faculty of Civil Engineering, Brno University of Technology, 60200 Brno, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Civil Engineering, Brno University of Technology, 60200 Brno, Czech Republic","institution_ids":["https://openalex.org/I60587646"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037345422"],"corresponding_institution_ids":["https://openalex.org/I60587646"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.4679,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.85282607,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"12","issue":"8","first_page":"1379","last_page":"1379"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11798","display_name":"Optimal Experimental Design Methods","score":0.9804999828338623,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9760000109672546,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.8324135541915894},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.6488618850708008},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6318334341049194},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5987446308135986},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5673013925552368},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.46433839201927185},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.4473261535167694},{"id":"https://openalex.org/keywords/series-expansion","display_name":"Series expansion","score":0.4452574551105499},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.366264283657074},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32950064539909363},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32784968614578247},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2333480715751648},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13099899888038635}],"concepts":[{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.8324135541915894},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.6488618850708008},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6318334341049194},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5987446308135986},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5673013925552368},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.46433839201927185},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.4473261535167694},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.4452574551105499},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.366264283657074},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32950064539909363},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32784968614578247},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2333480715751648},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13099899888038635},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym12081379","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081379","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1379/pdf?version=1597930639","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:https://dspace.vut.cz:11012/195719","is_oa":true,"landing_page_url":"http://hdl.handle.net/11012/195719","pdf_url":"http://hdl.handle.net/11012/195719","source":{"id":"https://openalex.org/S4306400317","display_name":"Brno University of Technology Digital Library (Brno University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60587646","host_organization_name":"Brno University of Technology","host_organization_lineage":["https://openalex.org/I60587646"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"pmh:oai:doaj.org/article:1cb6e4307bef47c599f88f6dab20220d","is_oa":true,"landing_page_url":"https://doaj.org/article/1cb6e4307bef47c599f88f6dab20220d","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 8, p 1379 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/8/1379/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12081379","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12081379","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081379","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1379/pdf?version=1597930639","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.49000000953674316}],"awards":[{"id":"https://openalex.org/G5250284559","display_name":null,"funder_award_id":"18-13212S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G6982375224","display_name":null,"funder_award_id":"FAST-J-20-6417","funder_id":"https://openalex.org/F4320321005","funder_display_name":"Ministerstvo \u0160kolstv\u00ed, Ml\u00e1de\u017ee a T\u011blov\u00fdchovy"}],"funders":[{"id":"https://openalex.org/F4320321005","display_name":"Ministerstvo \u0160kolstv\u00ed, Ml\u00e1de\u017ee a T\u011blov\u00fdchovy","ror":"https://ror.org/037n8p820"},{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W53543660","https://openalex.org/W1572480955","https://openalex.org/W1802152327","https://openalex.org/W1965453665","https://openalex.org/W1968969774","https://openalex.org/W1977441603","https://openalex.org/W1986686996","https://openalex.org/W1992801522","https://openalex.org/W1995565517","https://openalex.org/W2007535697","https://openalex.org/W2036773407","https://openalex.org/W2049774453","https://openalex.org/W2055591121","https://openalex.org/W2067478553","https://openalex.org/W2083415217","https://openalex.org/W2106735135","https://openalex.org/W2498977495","https://openalex.org/W2767420729","https://openalex.org/W2996330669","https://openalex.org/W3034350945","https://openalex.org/W3149050980","https://openalex.org/W6602162922","https://openalex.org/W6638189154"],"related_works":["https://openalex.org/W2135729712","https://openalex.org/W2032389377","https://openalex.org/W2392296723","https://openalex.org/W3186746902","https://openalex.org/W2561666027","https://openalex.org/W1978290145","https://openalex.org/W3105941352","https://openalex.org/W2952863483","https://openalex.org/W4300533772","https://openalex.org/W2044177028"],"abstract_inverted_index":{"The":[0,91],"paper":[1],"is":[2,25,53,83,93,111],"focused":[3],"on":[4,87],"Taylor":[5,74],"series":[6,75],"expansion":[7,76],"for":[8,71,95,119],"statistical":[9],"analysis":[10],"of":[11,13,38,59,73,77,80,121,131],"functions":[12,120],"random":[14,22,43,123],"variables":[15,44],"with":[16,105],"special":[17],"attention":[18],"to":[19,32,55],"correlated":[20,47,122],"input":[21,42],"variables.":[23,124],"It":[24,110],"shown":[26,112],"that":[27,113],"the":[28,126,132],"standard":[29],"approach":[30],"leads":[31],"significant":[33],"deviations":[34],"in":[35,48,103],"estimated":[36],"variance":[37],"non-linear":[39],"functions.":[40],"Moreover,":[41],"are":[45,117,135],"often":[46],"industrial":[49],"applications;":[50],"thus,":[51],"it":[52],"crucial":[54],"obtain":[56],"accurate":[57],"estimations":[58],"partial":[60],"derivatives":[61],"by":[62,98],"a":[63,68,106],"numerical":[64],"differencing":[65,81,115],"scheme.":[66],"Therefore,":[67],"novel":[69],"methodology":[70,92,134],"construction":[72],"increasing":[78],"complexity":[79],"schemes":[82,116],"proposed":[84,99,114,133],"and":[85,129],"applied":[86],"several":[88],"analytical":[89],"examples.":[90],"adapted":[94],"engineering":[96],"applications":[97],"asymmetric":[100],"difference":[101],"quotients":[102],"combination":[104],"specific":[107],"step-size":[108],"parameter.":[109],"suitable":[118],"Finally,":[125],"accuracy,":[127],"efficiency,":[128],"limitations":[130],"discussed.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
